Independent spanning trees (ISTs) have increasing applications in fault-tolerance, bandwidth, and security. In this paper, we study the problem of parallel construction of ISTs on crossed cubes. We first propose the definitions of dimension-adjacent walk and dimension-adjacent tree along with a dimension property of crossed cubes. Then, we consider the parallel construction of ISTs on crossed cubes. We show that there exist n general dimension-adjacent trees which are independent of the addresses of vertices in the n-dimensional crossed cube CQn. Based on n dimension-adjacent trees and an arbitrary root vertex, a parallel algorithm with the time complexity O(2n) is proposed to construct n ISTs on CQn, where n≥1.